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Mirrors > Home > ILE Home > Th. List > xpex | Unicode version |
Description: The cross product of two sets is a set. Proposition 6.2 of [TakeutiZaring] p. 23. (Contributed by NM, 14-Aug-1994.) |
Ref | Expression |
---|---|
xpex.1 | |
xpex.2 |
Ref | Expression |
---|---|
xpex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xpex.1 | . 2 | |
2 | xpex.2 | . 2 | |
3 | xpexg 4452 | . 2 | |
4 | 1, 2, 3 | mp2an 402 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1393 cvv 2557 cxp 4343 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-13 1404 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 ax-un 4170 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rex 2312 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-opab 3819 df-xp 4351 |
This theorem is referenced by: oprabex 5755 oprabex3 5756 xpsnen 6295 endisj 6298 xpcomen 6301 xpassen 6304 enqex 6458 nqex 6461 enq0ex 6537 nq0ex 6538 npex 6571 enrex 6822 addvalex 6920 axcnex 6935 ixxex 8768 shftfval 9422 |
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